If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

$A$ market with $3900$ operating firms has the following distribution for firms arranged according to various income groups of workers. If a histogram for the above distribution is constructed,the highest bar in the histogram would correspond to the class:

Income group	No. of firms
$150-300$	$300$
$300-500$	$500$
$500-800$	$900$
$800-1200$	$1000$
$1200-1800$	$1200$

Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are $6$ and $2$ respectively and $\sigma_A$ and $\sigma_B$ are their standard deviations,then:

The mean and variance of the observations $x_1, x_2, x_3, \ldots, x_{15}$ are respectively $2$ and $4$. If the mean and variance of the observations $y_1, y_2, \ldots, y_{10}$ are respectively $2$ and $5$,then the variance of the combined observations $x_1, x_2, \ldots, x_{15}, y_1, y_2, \ldots, y_{10}$ is

Consider a set of $3n$ numbers having variance $4$. In this set,the mean of the first $2n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3$. $A$ new set is constructed by adding $1$ to each of the first $2n$ numbers and subtracting $1$ from each of the remaining $n$ numbers. If the variance of the new set is $k$,then $9k$ is equal to .... .

The mean and variance of $7$ observations are $8$ and $16$ respectively. If the first five observations are $2, 4, 10, 12, 14$,then the absolute difference of the remaining two observations is